Average Error: 8.0 → 3.8
Time: 3.6s
Precision: 64
\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t = -\infty:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2} - 4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \le -1.2854101975700823 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2} - \frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \le 1.422832440737002 \cdot 10^{-44}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2} - 4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \le 2.2619286693938016 \cdot 10^{300}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2} - \frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2} - \left(t \cdot 4.5\right) \cdot \frac{z}{a}\\ \end{array}\]
\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}
↓
\begin{array}{l}
\mathbf{if}\;\left(z \cdot 9\right) \cdot t = -\infty:\\
\;\;\;\;\frac{x \cdot y}{a \cdot 2} - 4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\

\mathbf{elif}\;\left(z \cdot 9\right) \cdot t \le -1.2854101975700823 \cdot 10^{-43}:\\
\;\;\;\;\frac{x}{a} \cdot \frac{y}{2} - \frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\

\mathbf{elif}\;\left(z \cdot 9\right) \cdot t \le 1.422832440737002 \cdot 10^{-44}:\\
\;\;\;\;\frac{x \cdot y}{a \cdot 2} - 4.5 \cdot \frac{t \cdot z}{a}\\

\mathbf{elif}\;\left(z \cdot 9\right) \cdot t \le 2.2619286693938016 \cdot 10^{300}:\\
\;\;\;\;\frac{x}{a} \cdot \frac{y}{2} - \frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot y}{a \cdot 2} - \left(t \cdot 4.5\right) \cdot \frac{z}{a}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r1253796 = x;
        double r1253797 = y;
        double r1253798 = r1253796 * r1253797;
        double r1253799 = z;
        double r1253800 = 9.0;
        double r1253801 = r1253799 * r1253800;
        double r1253802 = t;
        double r1253803 = r1253801 * r1253802;
        double r1253804 = r1253798 - r1253803;
        double r1253805 = a;
        double r1253806 = 2.0;
        double r1253807 = r1253805 * r1253806;
        double r1253808 = r1253804 / r1253807;
        return r1253808;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1253809 = z;
        double r1253810 = 9.0;
        double r1253811 = r1253809 * r1253810;
        double r1253812 = t;
        double r1253813 = r1253811 * r1253812;
        double r1253814 = -inf.0;
        bool r1253815 = r1253813 <= r1253814;
        double r1253816 = x;
        double r1253817 = y;
        double r1253818 = r1253816 * r1253817;
        double r1253819 = a;
        double r1253820 = 2.0;
        double r1253821 = r1253819 * r1253820;
        double r1253822 = r1253818 / r1253821;
        double r1253823 = 4.5;
        double r1253824 = r1253809 / r1253819;
        double r1253825 = r1253812 * r1253824;
        double r1253826 = r1253823 * r1253825;
        double r1253827 = r1253822 - r1253826;
        double r1253828 = -1.2854101975700823e-43;
        bool r1253829 = r1253813 <= r1253828;
        double r1253830 = r1253816 / r1253819;
        double r1253831 = r1253817 / r1253820;
        double r1253832 = r1253830 * r1253831;
        double r1253833 = r1253810 * r1253812;
        double r1253834 = r1253809 * r1253833;
        double r1253835 = r1253834 / r1253821;
        double r1253836 = r1253832 - r1253835;
        double r1253837 = 1.4228324407370017e-44;
        bool r1253838 = r1253813 <= r1253837;
        double r1253839 = r1253812 * r1253809;
        double r1253840 = r1253839 / r1253819;
        double r1253841 = r1253823 * r1253840;
        double r1253842 = r1253822 - r1253841;
        double r1253843 = 2.2619286693938016e+300;
        bool r1253844 = r1253813 <= r1253843;
        double r1253845 = r1253812 * r1253823;
        double r1253846 = r1253845 * r1253824;
        double r1253847 = r1253822 - r1253846;
        double r1253848 = r1253844 ? r1253836 : r1253847;
        double r1253849 = r1253838 ? r1253842 : r1253848;
        double r1253850 = r1253829 ? r1253836 : r1253849;
        double r1253851 = r1253815 ? r1253827 : r1253850;
        return r1253851;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original8.0
Target5.8
Herbie3.8
\[\begin{array}{l} \mathbf{if}\;a \lt -2.090464557976709 \cdot 10^{86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a \lt 2.14403070783397609 \cdot 10^{99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if (* (* z 9.0) t) < -inf.0

    1. Initial program 64.0

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
    2. Using strategy rm

    3. Applied associate-*l*63.0

      \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2}\]
    4. Using strategy rm

    5. Applied div-sub63.0

      \[\leadsto \color{blue}{\frac{x \cdot y}{a \cdot 2} - \frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2}}\]

    6. Taylor expanded around 0 62.5

      \[\leadsto \frac{x \cdot y}{a \cdot 2} - \color{blue}{4.5 \cdot \frac{t \cdot z}{a}}\]
    7. Using strategy rm

    8. Applied *-un-lft-identity62.5

      \[\leadsto \frac{x \cdot y}{a \cdot 2} - 4.5 \cdot \frac{t \cdot z}{\color{blue}{1 \cdot a}}\]

    9. Applied times-frac5.5

      \[\leadsto \frac{x \cdot y}{a \cdot 2} - 4.5 \cdot \color{blue}{\left(\frac{t}{1} \cdot \frac{z}{a}\right)}\]

    10. Simplified5.5

      \[\leadsto \frac{x \cdot y}{a \cdot 2} - 4.5 \cdot \left(\color{blue}{t} \cdot \frac{z}{a}\right)\]

    if -inf.0 < (* (* z 9.0) t) < -1.2854101975700823e-43 or 1.4228324407370017e-44 < (* (* z 9.0) t) < 2.2619286693938016e+300

    1. Initial program 4.0

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
    2. Using strategy rm

    3. Applied associate-*l*4.2

      \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2}\]
    4. Using strategy rm

    5. Applied div-sub4.2

      \[\leadsto \color{blue}{\frac{x \cdot y}{a \cdot 2} - \frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2}}\]
    6. Using strategy rm

    7. Applied times-frac2.9

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{y}{2}} - \frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2}\]

    if -1.2854101975700823e-43 < (* (* z 9.0) t) < 1.4228324407370017e-44

    1. Initial program 4.2

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
    2. Using strategy rm

    3. Applied associate-*l*4.2

      \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2}\]
    4. Using strategy rm

    5. Applied div-sub4.2

      \[\leadsto \color{blue}{\frac{x \cdot y}{a \cdot 2} - \frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2}}\]

    6. Taylor expanded around 0 4.2

      \[\leadsto \frac{x \cdot y}{a \cdot 2} - \color{blue}{4.5 \cdot \frac{t \cdot z}{a}}\]

    if 2.2619286693938016e+300 < (* (* z 9.0) t)

    1. Initial program 60.1

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
    2. Using strategy rm

    3. Applied associate-*l*59.4

      \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2}\]
    4. Using strategy rm

    5. Applied div-sub59.4

      \[\leadsto \color{blue}{\frac{x \cdot y}{a \cdot 2} - \frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2}}\]

    6. Taylor expanded around 0 58.7

      \[\leadsto \frac{x \cdot y}{a \cdot 2} - \color{blue}{4.5 \cdot \frac{t \cdot z}{a}}\]
    7. Using strategy rm

    8. Applied *-un-lft-identity58.7

      \[\leadsto \frac{x \cdot y}{a \cdot 2} - 4.5 \cdot \frac{t \cdot z}{\color{blue}{1 \cdot a}}\]

    9. Applied times-frac7.6

      \[\leadsto \frac{x \cdot y}{a \cdot 2} - 4.5 \cdot \color{blue}{\left(\frac{t}{1} \cdot \frac{z}{a}\right)}\]

    10. Applied associate-*r*7.7

      \[\leadsto \frac{x \cdot y}{a \cdot 2} - \color{blue}{\left(4.5 \cdot \frac{t}{1}\right) \cdot \frac{z}{a}}\]

    11. Simplified7.7

      \[\leadsto \frac{x \cdot y}{a \cdot 2} - \color{blue}{\left(t \cdot 4.5\right)} \cdot \frac{z}{a}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification3.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t = -\infty:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2} - 4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \le -1.2854101975700823 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2} - \frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \le 1.422832440737002 \cdot 10^{-44}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2} - 4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \le 2.2619286693938016 \cdot 10^{300}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2} - \frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2} - \left(t \cdot 4.5\right) \cdot \frac{z}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020065 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :herbie-target
  (if (< a -2.090464557976709e+86) (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z)))) (if (< a 2.144030707833976e+99) (/ (- (* x y) (* z (* 9 t))) (* a 2)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

  (/ (- (* x y) (* (* z 9) t)) (* a 2)))